Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on and models another regular variation on the sub-cone , where is the $i…
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48 results for “regular variation”
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between Wasserstein DRO and regularization has been established in several settings, existin…
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to inaccurate and useless estimates of probabilities of joint tail regions. This pro…
Variational Pseudolikelihood for Regularized Ising Inferencecond-mat.stat-mech
I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The variational algorithm is more computationally efficient, and does a better job predicting out-of-sample correlations than regularized maximum pseudolikelihood inference as well as mean field and isolated spin pair appro…
Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We exhibit examples that illustrate the need for a more general model and discuss de…
While the impact of variational inference (VI) on posterior inference in a fixed generative model is well-characterized, its role in regularizing a learned generative model when used in variational autoencoders (VAEs) is poorly understood. We study the regularizing effects of variational distributions on learning in ge…
Study examines stability of image-reconstruction algorithms using variational regularization.
problem Stability and robustness of image-reconstruction algorithms in medical imaging.
method Review and novel stability results for -regularized linear inverse problems, focusing on .
result Guarantees Lipschitz continuity for small and Hölder continuity for larger in function spaces.
Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Modelcs.LG
Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
problem Estimating parameters in Gaussian location model with regularization.
method Ridge-regularized log-density-ratio estimation, variational and spectral approaches.
result Regularized variational estimator has lower risk with many observations, spectral estimator with fewer observations.
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in variational analysis for more than two decades while being largely underinvestigated. We …
Sparse regular variationstat.ML
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the positive orthant of the unit sphere. This measure gathers information on the localizat…
New variational approach to deep learning via gradient descent.
problem Non-robustness and poor out-of-distribution generalization in deep learning.
method Regularize variational neural networks using gradient descent's implicit bias.
result Strong in- and out-of-distribution performance achieved without additional hyperparameter tuning.
The paper studies the smoothness of critical points of variational integrals on Hessian spaces.
problem The study focuses on the regularity of critical points of variational integrals defined on Hessian spaces.
method The approach involves solving a fourth order nonlinear equation and analyzing the Hessian of the critical points.
result Smooth critical points with bounded Hessian are shown to be smooth provided their Hessian has small BMO.
Study on geometric variational problems for existence, regularity, and uniqueness of solutions.
problem Geometric variational problems, focusing on existence, regularity, and uniqueness of solutions.
method Formulated in Federer and Fleming's theory of currents, discussed the existence theory, and presented core ideas of the (interior) regularity theory for area-minimizing currents and optimal transport paths. Two original results on generic uniqueness of solutions were presented.
result Generic uniqueness of solutions for both Plateau's problem and optimal branched transport problem.
Improves Bayesian neural networks inference efficiency and accuracy.
problem Inflexibility of factorized structure in Dropout posterior.
method Introduces Variational Structured Dropout (VSD) with orthogonal transformation.
result VSD induces adaptive regularization and better generalization.
Proposes a variational approach to shallow neural networks, bypassing optimization.
problem Theoretical understanding and optimization of shallow neural networks.
method Replaces discrete training with a continuum variational surrogate, proving global well-posedness and regularity.
result Optimal parameter density can be obtained by solving a single linear system, achieving generalization error.
Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computationstat.ML
New method improves approximate inference for Bayesian models.
problem Approximate inference for high-dimensional Bayesian models.
method Entropic regularization of mean-field variational inference.
result Improved recovery of true posterior dependency.
New insights into tail behavior of heavy-tailed random vectors and processes.
problem Understanding tail behavior of aggregates of heavy-tailed random vectors.
method Analyzing multivariate regularly varying random vectors and Lévy processes.
result More than one large jump can determine tail behavior of aggregates.
Proposes a new method for continual learning in neural networks.
problem Challenges in applying sequential Bayesian inference to neural networks.
method Sequential function-space variational inference.
result Neural networks trained with the proposed method achieve better predictive accuracy.
Variational autoencoders learn unsupervised data representations, but these models frequently converge to minima that fail to preserve meaningful semantic information. For example, variational autoencoders with autoregressive decoders often collapse into autodecoders, where they learn to ignore the encoder input. In th…
A PDE approach to the existence and regularity of surfaces of minimum mean curvature variationmath.DG
Analyzes surfaces minimizing mean curvature variation using PDEs.
problem Finding surfaces of minimum mean curvature variation.
method Develops an analytic theory using partial differential equations.
result Establishes existence and regularity of minimizers.
Novel regularization for Vision Transformers improves model generalization and sparsity.
problem Improving generalization and sparsity in Vision Transformers.
method Likelihood-guided variational Ising-based regularization.
result Improved generalization and sparsity in Vision Transformers.
In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide results on the well-posedness and present algorithms for a numerical realizatio…
Variational Laplace improves Bayesian neural network performance without sampling.
problem Improving Bayesian neural network performance and calibration.
method Develops a new variational Laplace method for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms standard VI methods in test performance and calibration.
We introduce an elliptic regularization of the PDE system representing the isometric immersion of a surface in . The regularization is geometric, and has a natural variational interpretation.
Extends Campanato theory to multi-valued functions for geometric variational problems.
problem Regularity of multi-valued functions in geometric variational problems.
method Adapting Campanato's ideas to multi-valued functions, proving regularity theorems.
result Established regularity for multi-valued harmonic functions and stationary integral varifolds.
Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the application of regularization strategies. We present a mathematical framework unifying…
What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theorystat.ML
New framework explains deep neural networks using variational spline theory.
problem Understanding functions learned by deep neural networks.
method Developed a variational framework and function space.
result Deep ReLU networks are solutions to regularized data fitting problems over the proposed function space.
GAN+VER improves GANs by regularizing entropy to reduce mode collapse.
problem Mode collapse in GANs where the generator fails to capture all modes.
method Maximizing a variational lower bound on the entropy of generated samples.
result Significant improvement in evaluation metrics for real and generated samples.
Study compares L1 and VG sparsity priors in inverse problems.
problem Sparse regularization in inverse problems with incomplete or corrupted measurements.
method Compared L1 regularization with Variational Garrote (VG), a probabilistic method approximating L0 sparsity.
result VG often achieves lower minimum generalization error and improved stability in strongly underdetermined regimes.
New method prevents neural network breakdown by combining trimmed loss and variation regularization.
problem Outlier contamination in neural network training.
method Integrates transformed trimmed loss and higher-order variation regularization.
result Ensures robustness to outlier contamination with a high functional breakdown point.
We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and define a corresponding input-dependent additive noise data augmentation model. …
We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance. Furthermore, given -smooth data, we prove -regularity of solutions up t…
VAEs (Variational AutoEncoders) have proved to be powerful in the context of density modeling and have been used in a variety of contexts for creative purposes. In many settings, the data we model possesses continuous attributes that we would like to take into account at generation time. We propose in this paper GLSR-V…
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…
Denoising Diffusion Variational Inference: Diffusion Models as Expressive Variational Posteriorscs.LG
DDVI uses diffusion models for variational inference, improving latent variable model performance.
problem Improving variational inference in latent variable models.
method Introduces diffusion-based variational posteriors trained with a regularized ELBO.
result Outperforms alternative variational posteriors on various benchmarks and a biology task.
We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the gen…
A neural network learns a convex regularizer for better image reconstruction.
problem Improving image reconstruction in inverse problems.
method Adversarial training of a data-adaptive ICNN as a convex regularizer.
result The convex regularizer leads to better convergence and error reduction in image reconstruction.
A new method uses compressive autoencoders for image restoration.
problem Efficient regularization of inverse problems in computational imaging.
method Variational Bayes Latent Estimation (VBLE) with compressive autoencoders.
result VBLE achieves similar performance to state-of-the-art PnP methods but faster.
Proves ε-regularity for capillary surfaces in Riemannian manifolds.
problem Regularity of minimal surfaces with capillary boundary conditions.
method Uniform first variation control and ε-regularity theorems for varifolds.
result Capillary varifolds with bounded mean curvature and close to a capillary half-plane coincide with a properly embedded hypersurface.
Proposes learning regularization strength directly from data.
problem Computational expense and data reduction in grid search for deep learning hyperparameters.
method Modified Evidence Lower Bound (ELBo) objective for model selection on full training set.
result Comparable heldout accuracy to grid search with less compute time.
Benefiting Deep Latent Variable Models via Learning the Prior and Removing Latent Regularizationcs.LG
New findings suggest latent regularization is unnecessary for high-quality image generation.
problem Improving image generation quality without latent regularization.
method Investigated the effect of latent regularization on image generation using learned priors.
result In the case of a sufficiently expressive prior, latent regularization is not necessary and may harm image quality.
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various probability measures, as in the Wasserstein barycenter problem, or to carry out param…
A new method for VAEs improves latent space disentanglement without violating probability laws.
problem Improving latent space disentanglement in VAEs without violating probability laws.
method Developed a Renyi VAE with a conditional distribution not learned, using Singular Value Decomposition for evaluation.
result Improved latent space disentanglement without violating probability laws.
The paper analyzes rates for a modified gradient descent method using Stein variational gradients.
problem Improving the accuracy of gradient descent methods for complex target distributions.
method Derives finite-particle rates for regularized Stein variational gradient descent (R-SVGD).
result Establishes explicit non-asymptotic bounds for time-averaged empirical measures.
RegVar quantifies uncertainty in deep learning networks by measuring sensitivity to regularization.
problem Uncertainty quantification in deep learning networks, especially for large networks.
method RegVar method based on variation due to regularization, implemented during fine-tuning phase.
result RegVar provides rigorous uncertainty estimates that recover Bayesian deep learning approximations.
We accelerate CNF by reducing ODE truncation errors with polynomial regularization.
problem High computation cost of CNF due to large truncation errors in solving ODEs.
method Add polynomial regularization to approximate ODE trajectories with polynomial functions.
result 42.3% to 71.3% reduction of NFE on density estimation, 19.3% to 32.1% on variational auto-encoder.
In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised learning in a continuous-domain hybrid search space with gTV regu…